Empirical Individual Assignment - Time Series Regression Analysis

Task

The objectives of this assignment are to test your understanding of the various data modelling (time series) techniques covered in the course, expose you to the kind of work you may encounter in your professional career and test your ability to write reports that have technical depth but can be understood by a non-technical audience (such as potential clients).

You are working to undertake a research project for a multinational consultant firm. This project investigate how the fluctuations of oil, gold and Bitcoin prices affect the performance of top largest stock markets1, including New York Stock Exchange, Nasdaq, Japan Exchange Group (Tokyo Stock Exchange), Shanghai Stock Exchange, Hong Kong Exchanges and Clearing, Euronext, London Stock Exchange, Shenzhen Stock Exchange, BSE Limited, National Stock Exchange of India, TMX Group (Toronto), Deutsche Börse (German Stock Exchange), Six Swiss Exchange, Korea Exchange, Nasdaq Nordic Exchanges, Australian Securities Exchange, Taiwan Stock Exchange, B3 - Brasil Bolsa Balcao, Johannesburg Stock Exchange, and BME Spanish Exchanges.

You will get the information of which stock exchange market is assigned to you from your lecturer.

You need to collect monthly data of crude oil, gold and Bitcoin prices and stock market index of the assigned stock exchange market from Jan 01, 2015 to Dec 31, 2020. You should use adjusted close price for these variables.

Data analysis results must be completed using SPSS or Excel (for Breusch-Godfrey test and Newey-West standard error estimates), the statistical software packages adopted in this course.

1. Introduction

2. Descriptive Statistics

3. Model Analysis

4. Overall Conclusion

5. References

In this part you set the scene for the research.

Discuss overview about the stock exchange market is assigned to you

Explain why oil, gold and Bitcoin prices are important for understanding stock market performance.

You need to point out clearly the research objective in the introduction.

Provide information of the data that you use in the report: discuss data collection, cleaning data process and how variables are measured.

In Part 2 you will provide an overview of the time series data assigned to you.

(i) Draw line charts over time of the prices and the log-prices for all variables including crude oil, gold and Bitcoin prices and stock market index. For convenience you can draw multiple line charts in one figure.

(ii) Calculate return and log-return for crude oil, gold and Bitcoin and stock market index. Draw line charts over time of the return and the log-return for all variables. The return of xt is calculated by xt - xt-1. The log-return of xt is calculated by log(xt) - log(xt-1). For convenience you can draw multiple line charts in one figure.

Empirical Individual Assignment - Time Series Regression Analysis

(iii) Based on these figures, comment on the components of time series data and any features of interest. Do not use numerical summaries but comment only by the visual analysis of the figures.

(iv) Statistically describe the stock market index, crude oil, gold and Bitcoin prices including mean, median, minimum, maximum and standard deviation.

(v) Checking potential multicollinearity problems of variables including crude oil, gold and bitcoin prices by using relevant approaches.

In Part 2, you will analysis several time series models. Using Durbin Watson test or BreuschGodfrey test to check no serial correlation assumption in all models. If there is the presence of autocorrelation in your estimates, using relevant methods to fix this problem. Present only the estimation results after fixing autocorrleation (if necessary). Present the estimation results in neatly formatted tables (all the estimation results, such as coefficient estimates, standard errors, t-values, p-values, R2 and number of observations should be included in Tables).

Denote the statistical significance of the estimate by the conventional star notation (*** pvalue <0.01, ** p-value < 0.05, * p-value < 0.1; standard errors are presented in parentheses). We put the template of result tables at the end of the instruction.

where logSt, logCt, logGt and logBt denote log-prices of stock, crude oil, gold and Bitcoin prices, respectively.

(i) Estimate the Model (1). Interpret all significant variables results.

(ii) Re-estimate Model (1) by adding a linear trend variable. Interpret all significant variables results. Compare these estimation results with those of (i).

(iii) The January effect is a hypothesis that there is a seasonal anomaly in the financial market where securities' prices increase in the month of January more than in any other month (Ciccone , 2013).To test January effect, you need to generate dummy variables for 12 months. Re-estimate Model (1) by adding these dummy variables, keeping January dummy as a base month. Based on your analysing results, discuss whether you find significant January effect in your assigned stock market.

Note: Results from (i), (ii) and (iii) can be presented in one Table with the template provided at the end of the instruction. However, the discussion of questions (i), (ii) and (iii) should be put in separate sections.

where logRSt, logRCt, logRGt and logRBt denote log-returns of stock, crude oil, gold and Bitcoin prices, respectively.

(iv) Estimate the Model (2). Interpret all significant variables results. Compare these estimation results with those of (i).

(v) Re-estimate Model (2) by adding a linear trend variable. Interpret all significant variables results. Compare these estimation results with those of (iv) and (ii).

(vi) Re-estimate Model (2) by adding month dummy variables, keeping January dummy as a base month. Based on your analysing results, discuss whether you find significant January effect in your assigned stock market. Compare these estimation results with those of (iii).

Note: Results from (iv), (v) and (vi) can be presented in one Table with the template provided at the end of the instruction. However, the discussion of questions (iv), (v) and (vi) should be put in separate sections.

(vii) Compare the results from (i) – (vi), evaluate which specification provides the best estimation results for your research. And explain why this is the best result. Provide crystal clear interpretations of the results.

(viii) Can you recommend any other variables to be included into the model? Explain your recommendation(s).

Part 4: Overall Conclusion

In this part you will provide an overall conclusion for the manager based on the analysis you have done in Part 1, Part 2 and Part 3. You are allowed to provide additional information/analysis, but should not exceed the word limit. Propose relevant policy recommendations based on your analysis to your manager. Your manager of the consultancy firm is an expert in this field, but he/she is not an econometrician. Write Part 4 in such way that it is understandable for your manager. Assume the manager will only read Part 4 of the report.